How to Make a (Safe) Black Hole in Your Garage

As you know, quantised inertia predicts that a new kind of propulsion can be extracted from charged capacitors. This is essentially the Casimir effect and charging the cathode so that electrons stream across to the anode pushing the whole thing a little bit more than expected. In 2021 (see also my 2024 book) I derived this thrust using dimensional and physical arguments to be

F = 0.00014 x IA/d^2

where I is the Fowler-Nordheim leakage current, the A is plate area and d is the plate separation. This predicts the thrust measurements from several laboratories, one in California (Becker and Bhatt), Virginia (IVO Ltd), Italy and the one I set up with Richard Arundal at Plymouth University, and the thrust has also been seen in a few high-powered 'garages' or home labs. I have recently repeated and improved the derivation of this that I had before, but recently Morgan H. Lynch suggested to me another way to derive the same formula that is more speculative, but is rather elegant and couples the down to Earth component of this with black hole physics.

Imagine a small black hole, shown above. It is emitting Hawking radiation of power P (the red arrows). The total force coming off it is P/c, where c is the speed of light. Now imagine someone extremely brave goes up to the event horizon and puts a capacitor (grey //) on it so that the cathode is just on the horizon. What would the force on the electrons be? It would be P/c times the ratio between the plate area (A) and the area of the whole black hole radius d, so

F = PA/(4pi.cd^2)

Now let us imagine that the leakage current observed in the capacitor is equivalent to Hawking radiation. The mass energy flux rate is P = (I/q)mc^2, where q and m are the charge and mass of an electron, so

F = (mcIA)/(4pi.qd^2)

Now let's just put the known numbers in here and see what happens.

F = 0.00014 x IA/d^2

Compare this with the formula I derived before. The same! In other words, in some sense, that is not entirely clear yet, the QI thrust capacitor is analogous to a black hole. In a sense it is, because, for a highly accelerated object like an electron, the Unruh waves are short enough to be damped by the plates so the area between the plates is a sub-vacuum bounded by a metal horizon. Not a million miles from the concept of a black hole.

After I told him this my son asked if there was any danger. The answer is no. It's just another horizon. They form whenever anything moves (strictly - accelerates) and based on billions of years of experience they do not swallow the universe. So you too can make a 'black hole' in your garage.

By the way, I'm now making short videos about QI and related issues. The videos are available on my YouTube channel:

https://www.youtube.com/channel/UC0LWcVMLjdw7duQRVsqzZNQ

References

McCulloch, M.E., 2021. Thrust from symmetrical capacitors using quantised inertia. Research Gate: https://www.researchgate.net/publication/353481953_Thrust_from_Symmetric_Capacitors_using_Quantised_Inertia

Light is a Quantum Pressure Wave?

 I've been writing a new book, made up so far of mini-papers, but I've been sticking them all together and two of the bits taken together are pretty exciting so I'm writing a paper on that. The paper has four steps to it:

Step 1. Thesis. I've shown that light looks like a sound wave in the quantum background. When you assume that, it predicts a speed that agrees with the speed of light within 10%, which is the uncertainty of some of the parameters I'm using anyway. So that was my initial observational test and it passed.

Step 2. Based GR. If you apply quantised inertia to this, you get the equation for the propagation of light from general relativity. It predicts general relativistic effects not from curved spacetime, but from the inhomogeneity of the quantum background around matter. This is a much more scientific model than curved space because you can see both the effect (light bending) and in principle also the cause of it (inhomogeneities in the quantum background).

Step 3. A Test. This model predicts that if you fire a laser through a cavity then the light should slow down. That is a test that can be done quite easily and as I recall was done by Harold White once. He fired a laser through an emdrive just for the heck of it and saw anomalous results.

Step 4. Application. What this means is that by engineering the vacuum (not sure how yet) we should be able to increase the speed of light and travel faster than the usual light speed limit. Perhaps this already happens in some parts of deep space?

If I can get this past the reviewers or censors this will be a great paper. It represents conceptual progress, but is also testable and applicable. If I can't publish it that way, I'll just go to Plan B and continue with the book. It was supposed to be about time, but that's a concept so big to think about, that a lot of other things are dropping out along the way.

A Tale of Two Satellites

In March 2025 SpaceX launched a Rogue Space Systems cubesat with an IVO Ltd Quantum (QI) Drive on it. Up till Christmas I was monitoring its trajectory, almost every day and it did seem to push up by about a few metres when it seemed from personal communications that they had turned it on, but analyses like this are very subjective.

Unfortunately, as you may know, there was a engineering glitch so the thruster could not be turned on for more than a minute before problems arose, so the hoped-for orbit raise of kilometers did not come to pass. Which leaves us in a less than ideal position. Can we see if there is QI thrust? We probably cannot do this for certain, but I collected a lot of data from SatNOGS DB (nearly every day for several months) so it makes sense to see what we can get from it.

They always say "Don't compare yourself with others," but in science that is a valid method. One thing we can do is to use a control: a similar satellite without a QI drive. The IVO Sat (Norad ID = 63235) had a close twin brother (Norad ID = 63220) which was the same shape and mass and was launched by the same Falcon 9 rocket into about the same orbit. So, we can look at their fall over the last three months and see if the IVO Sat fell less than the control satellite. IVOsat fell from 506.3 km on 30/9/25 to 501.42 km on 30/12/25, a fall of 4880 metres. The other satellite fell from 504.98 km to 499.5 km so a fall of 5480 metres. Therefore the IVOsat fell 600 metres less over three months. Does that mean the QI Drive thrust it up by 600 meters over that time? Possibly. Is that the rise we expect give the thrusting they did?

The thrust generated by the QI quantum drive was expected to be 1.75 mN and the mass of the satellite is 20 kg which means that the along track acceleration (a) will be

a = F/mass = 0.00175/20 = 8.75x10^-5 m/s^2

Since I happen to know that the typical burn time was about a minute, and if we assume it was fired once every other day, a reasonable guess, then the change in speed per day (dv) is

dv = 8.75x10^-5 x 60 /2 = 0.002625 m/s

The change in height (dH) is

dH = 2.dv.sqrt(r^3/GM) = 5 metres per day

The observed rise (compared to its twin) was 600 metres in 90 days, which is 6.6 metres per day. Therefore the IVOsat moved up relative to its twin satellite by about the height you might expect if the Quantum Drive was being fired every other day for one minute on average. It looks plausible, but it could be that the drive was generating a Lorentz force and pushing off the Earth's magnetic field. My calculation of the Lorentz force suggests it's too small but I do not have detailed knowledge of the circuitry in the drive. We had hoped to have thrust large enough to avoid ambiguities like this but that has not been the case.

If this QI Quantum Drive was indeed thrusting then it means a radical change to the entire satellite industry because we can now have onboard thrusters that are silent and do not need to carry heavy fuel so they will last much longer, but we are not in a position to say that yet. Anyway, a big thank you to IVO Ltd, Rogue Space Systems and SpaceX who got the test up there (an amazing feat in itself) and have produced some results. I hope they will soon make a more detailed press release on it.

Elephants in the Room (JuMBOs)

The fantastic news is that the journal Astronomy has just peer-reviewed, accepted and published my new paper on the Jupiter Mass Binary Objects (JuMBOs). Since it was an invited contribution I do not have to pay £1000 to make it open access.

As you know, quantised inertia predicts there is a minimum acceleration in nature of around 2x10^-10 m/s^2. This is such a small acceleration that it would take the lifetime of the universe to get from zero to the speed of light (there a big clue to something right there). How do we test this? Look where nature tests the limit. Stars at the edge of galaxies are doing that and move faster to stay above this minimum, that’s why they orbit faster than expected, not because they contain invisible dark matter. Galaxy clusters, wide binaries and even our nearest neighbour Proxima Centauri all hover just above this limit and these are all on different scales, thus proving that the reason is not dark matter since this has to be spread out specifically on galactic scales.

When a paper was published by McCaughrean and Pearson (2023) finding what looked like 42 wide binaries in the Orion nebula, I thought “I’ll bet they too hover just above the QI minimum.” Sure enough, when I checked, they did! QI never fails. Hence the plot below which shows the separation of each binary (x axis) against the orbital acceleration (y). As they get wider, they still stay above the minimum predicted by QI (red line, but see the caveat below).

I always have the confident feeling on testing QI that it is going to work, but it is still a great thrill when it does. There are a couple of data points that are strictly below the QI minimum but this minimum also has an uncertainty, mostly due to uncertainties in the cosmic scale.

In any good paper, there’s always a testable prediction and a caveat. The QI prediction is that the widest of these binary objects should be orbiting up to 70 metres per second faster than expected and this prediction could be tested by the HARPS (High Accuracy Radial Velocity Planet Searcher) telescope which is used to spot exoplanets and can determine orbital speeds, they say, to an accuracy of 1 m/s. The main caveat is that we need to find more of these JuMBOs to be sure they are binary objects and not just coincident objects. Their being just random coincidence is very unlikely, as stated in the observational paper, because the line of sight points out of the galaxy so there isn't much situated behind them, but you know sceptics! I've been through quite a long, and useful, review process on this one so it's great to end the year with a success.

If you liked this, find much more at my patreon site: https://www.patreon.com/OneSteptoTauCeti

References

Pearson, S.G. and M.J. McCaughrean, 2023. Jupiter mass binary objects in the Trapezium cluster. https://arxiv.org/abs/2310.01231

McCulloch, M.E., 2026. Jupiter Mass Binary Objects Show a Minimum Acceleration. Astronomy, 5(1), 1. https://www.mdpi.com/2674-0346/5/1/1

3I/Atlas Bound?

This month's great leap forward is that I have written a fortran model to simulate complete QI dynamics for the first time. The great thing about having a fortran model is that you can run experiments with it. I've suspected for a while that these interstellar comets like Oumuamua, Borisov or 3I/Atlas are actually bound to the Solar system, or 3I/Atlas at least. This was based on little more than my QI intuition that objects at low acceleration, in other words out in the boondocks, tend to be bound when they are not supposed to be. This is because at low accelerations QI reduces the inertial mass and also the centrifugal force, so there's less tendency than expected for objects to go in straight lines and with a circular orbit, this means less tendency to veer off into deep space. Galactic edge stars and wide binaries are unexpectedly bound. Unexpected unless you know about QI.

As a test, I initialised 3I/Atlas at its perihelion, taking the data from the JPL Horizons website and then modelled it as it shot off into the outer solar system. With Newtonian physics it kept on going and was an interstellar comet as everyone expects. With QI, it first slowed down in its trajectory as it lost inertial mass and was more easily attracted back to the Sun, a bit like the Pioneer craft. This was very obvious after about 100 years. Then at about 1500 AU distance it came to a virtual stop and started on a very slow turn-aroud back to the Sun. On other words. Despite its present breakneck speed, of 68,000 m/s, it's bound and someday it will be back. This is as much of a shock to old physics as when Rutherford fired alpha particles at atoms in gold foil and saw them bounce back thus proving the existence of the hard central nucleus, or the day an Australian native threw away a bent stick and it came back and hit him on the head.

This realisation with QI that 3I/Atlas is bound solves so many of the problems that have been pointed out by Avi Loeb. It arrived in the plane of the ecliptic, and the random chance of that was very low. More importantly, 3I/Atlas is so massive: one million times the mass of the first 'interstellar' object Oumuamua and 1000 times the mass of Borisov. It is just crazy that we should see something so big. We should see 1000 Oumuamuas before we see one Borisov, and 1000 Borisovs before one 3I/Atlas. But 3I/Atlas is what it is. It would be a shock if there is so much mass in interstellar space. It is far easier to assume that 3I/Atlas is part of the Solar system, just coming in from the Oort cloud, if that exists. I suspect it might be closer in than expected. This accounts for it being in the ecliptic plane - it is just derived from the same condensed, flattened cloud that all the planets are, and its huge mass is no longer a mystery. I love simplifications, and QI always provides a few for free.

So is 3I/Atlas bound? Newton says no. QI says yes, and remember that the data is with QI in these low acceleration regimes. QI predicts galactic edge stars and wide binaries, whereas Newton does not without a ridiculous amount of arbitrary (dark) help. Anyway, this is bound to change our view of the Solar system.

The Sark Foundation

Well here's an update for you. For much more on all these topics, please see my patreon (link below). 

I'm part of a team submitting a proposal for a European Research Grant. I'm not getting that excited about it yet because, even if we get the funds, the work won't start till mid 2027, but it would be 10 million euros shared between four Principal Investigators. It involves trying to combine quantised inertia with a theory of time called 3d time. QI predicts that the time perceived by an object depends on the degree of interaction it has with its environment (no change = no time), so it predicts that time progresses differently for quantum systems (with few interactions), macro systems (lots of interactions) and cosmic systems (few interactions). Gunther Kletetschka's 3-d time kind of assumed that tripartite rule so there may be testable links there and also, I hope, more efficient ways to get to QI thrust.

I've co-written a new book with Ed Dutton on ancient civilisations, so let's see if the publisher accepts it. We're saying that every so often the Earth's magnetic field collapses causing havoc and cosmic dust.

The IVO satellite is still up there testing the QI quantum drive. As I said on X a while ago, something is going on that is encouraging, but I can't tell you anything. Bad news travels at light speed, good news is subject to NDAs. Nothing conclusive, but I'm pretty happy with the way it is going. The process has proven difficult, but that is not a surprise. There's a reason 'brain surgeon' and 'rocket scientist' are both used to refer to people who can do difficult things. IVO and Rogue are doing it.

What I'm doing at the moment is working on various theoretical papers and books. I've resubmitted the paper on how QI predicts the Jupiter Mass Binary Objects, written a paper deriving relativity from information theory and a paper deriving light as a sound wave on the quantum vacuum... It works!

I'm also revisiting the Floating Brick concept, and it occurred to me that there has already been an observation of something similar. This is in a paper by Linn et al. (2020) in which they warmed up two cubes containing photonic crystals to 575K (302degC). One with a uniform cross section and one with tungsten rods within, separated by about a micron. There was a difference. The block with the rods in it, emitted about 8 times the thermal radiation allowed by Planck's radiation law, far too much, and at the wavelength of the separation of the tungsten rods. This is what QI predicts for small cavities. As you confine information, heat must be released and in Linn's case it certainly was. I've been doing a calculation to predict what size of cavity you'd need to produce enough Unruh radiation for it to lift off, and, theoretically, it should be doable. The Floating Brick again!

I'm also writing a new sci-fi, this time explaining how QI would best be applied in a sort of Manhattan project, if, for example, a comet the size of 3I/Atlas was headed for Earth. I'm having fun writing it, probably because I've just promoted myself to head a large Scientific Foundation based on the island of Sark and we have just launched our first test 'LeviCube' into space.

For more updates like this please subscribe to my patreon: https://www.patreon.com/OneSteptoTauCeti

To read along with The Sark Foundation, subscribe to: https://www.patreon.com/BeyondtheBlueSky

References

Lin, SY., Hsieh, ML., John, S. et al. An In-situ and Direct Confirmation of Super-Planckian Thermal Radiation Emitted From a Metallic Photonic-Crystal at Optical Wavelengths. Sci Rep 10, 5209 (2020). https://doi.org/10.1038/s41598-020-62063-2

The Quantum Time Machine (A QI-Themed Short Story)

Dr Filius Apry had realised years ago, something that no-one else had: Heisenberg's uncertainty principle allows time travel. Well... sort of. To avoid bothering you with the maths, the principle can be written like this

(uncertainty in time) x (uncertainty in energy) = a constant.

That means that if the uncertainty in energy decreases then the uncertainty in time has to go up, and that means you can see into the future and the past. After realising this he had made contact with the crypto millionaire Bo Zanden who was willing to fund it, and at his university he had built a cryostat, a tough glass sphere in which there was a near vacuum cooled very close to absolute zero. You see, the only way to make sure that the uncertainty in energy is tiny, and to dilate time, is to make sure that the energy is tiny as well, i.e. freeze it down to close to absolute temperature, and that he did.

It was three years later, with Bo pestering him about the imminent deadline, that he finally switched it on. It was a little earlier than he would have liked so health and safety had not been confirmed, and he looked into the void he had created, a few pico-Kelvins from absolute zero. Before he had even pressed the switch to release a ball from a grip at the top of the cavity, the ball appeared to be falling, but only a transparent version of itself, spread out as a stream, like a ghostly column. When he actually pressed the switch the ball fell in full intensity and for a while after it had hit the bottom of the glass sphere, the ghostly stream of balls lingered. Inside the void he had just seen the past, present and future all mashed up together. He quickly looked around to check that no-one was watching, and then did the dance he usually did when he had a major breakthrough.

He looked again at the void, and moved a little closer this time. There was his face in there, but all mashed up! It was only a very indistinct image, ghostly, but unmistakably him.

"It must be a reflection," he said, unconvinced.

It only then became clear to him that something was pulling him towards the void, an inexorable force, remarkably strong. He had moved too close. He grabbed the desk, but the void was pulling him in, and he could not resist any more than we can resist the downwards force of gravity. He had helpfully placed the off switch too far away. As he realised he was going to die, he coolly worked out what was happening. A dilation of time was also a feature of relativity, of gravity. He had effectively created a gravitational source. But, why was the image of himself not of full intensity? That meant it was not inevitable that it would occur. There was a way out! But how? Then the image of himself faded, and few seconds later just as the glass shell was about to break around the vacuum a fuse blew and saved his life.

Shaken and back at his desk, he collapsed with a sign of relief and sent a quick email to Bo Zanden. "It works, in more ways than one, but it came down to the wire!" Being on the cutting edge is certainly exciting, if you can survive it.

If you enjoyed this please keep me afloat to do more physics and writing by contributing the cost of a coffee using paypal (michael.e.mcculloch@gmail.com) https://www.paypal.com/uk/home Thanks. I'm having trouble with other options at the moment.

The Journal of Empiricism

When I used to work at the UK Meteorological Office, I was often in their library when work permitted. That was in the old building in Bracknell, a building which no longer exists. One of my favourite reads was The Meteorological Magazine, which was devoted solely to reporting interesting observations, like the early journals of the Royal Society in the time of Newton and Hooke. I loved reading that because the anomalies gave me something to think about: a large water spout was seen near Bali, St Elmo's fire in the Sargasso Sea, a freshwater layer on the ocean, made it hard for boats to make way... Here were genuine phenomena, mysteries that no-one had ever solved, and maybe I could solve them?!

By the time I found it and had read a few articles I distinctly remember asking at the desk for the more recent issues and I can still remember my disappointment when Yunus the friendly librarian told me apologetically it had been discontinued in 1994.

By that time anomalies were becoming undervalued, and this was part of a decline that has occurred throughout science. Technically we have better observations than ever, but what good are they if the latest compulsory solution is enforced on the subject from above for reasons of social control (climate), profit (medicine) or the furthering of existing research programs? (strings, dark matter).

So, in 1994 The Meteorological Magazine was closed down, and it was replaced by the business-like Meteorological Applications. The same thing has happened in wider physics, but to reinvigorate the field at a deep level what we should do is to make a new journal like those of the early Royal Society. Allow those good at observing to publish freely without forcing them to fudge a solution, and allow those who love to ponder deeply to freely publish their suggested solutions. First look, then think. The old symbiosis would return and we'd advance far faster.

JoE: the Journal of Empiricism?

PS: If you like this please come over and support me (£3/month, or more if you can) at patreon. It makes possible my independent research program: https://www.patreon.com/OneSteptoTauCeti

Demysticon 2025 in Sesimbra

As you may know I've just attended a conference in Sesimbra, Portugal. I was invited to speak on QI at the Demystify 2025 conference and it has been a tremendous experience, both because of the beauty of this area (my hotel balcony overlooked the turqoise sea and the seafood was fantastic) and especially the stimulating talks and conversations I have had. I won't give details of the talks, because they will appear online soon, but I'd like just to provide some highlights.

The first talk was by Alexander Unzicker who proposed, half in jest, a Department of Scientific Efficiency (DoSE) to get rid of all the grift in physics and eliminate physical constants. Then Eric Lerner outlined some of the problems with the Big Bang theory such as the Lithium problem: there is only 1/3 as much as there should be. Patrick Van Raes presented two ideas from Robitaille, the Liquid Sun model (the problem is: how can you get fusion then?) and R's theory that the Cosmic Microwave Background radiation is actually being emitted from the ocean which explains why it has only been seen in satellites close to the Earth like COBE and not in those far away like Planck. There was then a spirited argument especially from M.L Corredoira, because some claim that Planck has seen it but they just didn't bother to put it in the paper because everyone assumed it was true anyway.

Then Indranil Banik showed that you can explain the Hubble tension (the higher redshift of nearby supernovae) if you assume we are in a local void (a big hole) so that nearby over-densities are pulling everything out of the void more strongly than expected. He has been looking at Baryon Acoustic Oscillations which are frozen sound waves left over from the early universe that provide a standard ruler. Banik & Kalaitzidis (see references) predicted how big they should appear at each redshift. Only by assuming we're in a local void, as found in local galaxy undercounts, did they get agreement. This is independent evidence for the local void, and happens to solve the Hubble Tension because gravity pulls matter out, increasing the local Hubble constant. He gets some pushback from people using the cosmological principle (the cosmos must be uniform on big scales), but I think that argument falls flat. I don't see the problem with a local hole and the Hubble Tension is a major issue.

Then Andre Assis, lovely guy, said that the Cosmic Microwave Background (CMB) is actually evidence against the Big Bang, because its temperature was predicted far better by the earlier steady state theories than by the Big Bang models. Andre later kindly advised me to relax a bit, and also to study the electromagnetism of Weber, which I like already because it gets rid of the abstract concept of the field.

Alexander Unzicker then spoke on the Variable Speed of Light (VSL) cosmology. A curved space with a constant c is equivalent to a flat space with a varying c. I admire this guy more than any other physicist of our time, but of course, as he admits, even if the standard form of VSL is true it still agrees with general relativity so we are back to all the problems with galaxy rotation. Nevertheless, I agree the VSL is the way to go, it fits better with QI and is directly testable, unlike curved spacetime.

My talk went well. I presented my QI cosmology with a varying G. One guy asked if that means I can solve Sagan's faint young sun paradox. The early Sun, under standard physics should have been dimmer, but oddly the Earth was not generally a snowball at that time. Indeed, a higher G in the past leads to more intense stars: more confinement, more fusion, but Indranil Banik suggested it would make them burn too quick (unless c varies as well?) Interestingly, a varying G would also mean a smaller Earth in the past.

Then an interesting and bold talk from Unnikrishnan who claimed that he has disproved special relativity by doing, for the first time, a one-way speed of light test. He claims that c depends on the observer's motion. I need to read his paper before commenting on that one! (see his comment below).

As a finale I had a chat with Indranil Banik that was so interesting and covered so much ground (from quantum thrusters, to Milky Way satellite galaxies to how to build a cosmology) that we talked from 7pm to 3am. He said he might invite me to talk at the Cosmology Institute in Portsmouth. This was the overall hope of this conference, which was organised brilliantly by Anastasia Bendebury and Shilo DeLay (on X, @demystifysci): to build a bridge between the mainstream and mavericks.

References

The Conference website: https://demystifysci.com/demysticon-2025

Unzicker's first talk at the conference: https://www.youtube.com/watch?v=bOdyPNYo8Po

Indranil's Hubble Tension paper: https://dx.doi.org/10.1093/mnras/staf781

No Need for Dark Galaxies

Recently, a few people on X pointed out to me a paper by a Chinese group (Lui et al., 2025) who have been monitoring neutral hydrogen outside the Milky Way disc and noticed what they call a compact gas clump, named poetically: AC G185.0-11.5. It is a swirling mass of hydrogen that somehow stays together. The mainstream of course proposed adding as much dark matter as needed to keep it together within the remit of general relativity, and called it a 'dark galaxy' (there are others like this, such as Dragonfly 44), but we know how to do testable physics, so we can do better.

From a paper I wrote in 2012 (see the reference), quantised inertia (QI) predicts that the velocity of the material at the edge of a system at very low acceleration has to be just large enough to keep the acceleration above the cosmic minimum (2c^2/Cosmic_scale), so it will be

v = (2GMc^2/Cosmic_scale)^0.25

So let's see if QI can predict this newly-observed system (you know it will, or why would I be writing this with such a confident air!). Its gas and dust mass was given in Liu et al. (2025) as ranging from a possible 3x10^7 to 4.7x10^8 solar masses, and the cosmic (Hubble) scale is 8.8x10^26 m, so using the QI equation above, the predicted orbital speed has a low of 30 km/s and a high of 58.9 km/s, so let's say 44.5 +/- 14.5 km/s.

So what do Lui and crew say is the observed rotational speed? Drum-roll... It is 42.2 +/- 2 km/s. QI predicts it well. It correctly predicts Dragonfly 44 as well (I wrote a blog on that one in 2016). I always thought dark matter was a load of hot gas, but now it seems it's not even that! QI for the win.

By the way, for far more frequent updates like this please subscribe to my patreon account here: https://www.patreon.com/OneSteptoTauCeti

References

Liu et al., 2025. Discovery of a high-velocity cloud of the Milky Way as a potential dark galaxy. Science Advances, Vol 11, Issue 16. https://arxiv.org/pdf/2504.09419

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics & Space Sci. Vol. 342, No. 2, 575-578. https://arxiv.org/abs/1207.7007

The End of the Dark Age of Physics?

Physics has been in what we might call A Dark Age since the 1960s, with fashions such as quarks, space-time (general relativity took over in the 1960s), strings vibrating in 11 dimensions, dark matter and dark energy. The problem with concepts like these is that there is no way to test them directly. You can test space-time by passing things through it, but that is circular because you designed it to model that in the first place. How can you break the loop and get to view it directly? You can’t. So how can you be sure there’s not some other model that works better? General relativity failed to predict every galaxy rotation ever seen, yet is still popular!

I prefer to have physics that is successful, and testable all the way down, or as far down as possible. So quantised inertia re-grounds physics on what we can see and test directly, namely acceleration and quantum fields (Unruh radiation). I can now say the latter is observable because Lynch et al. (2021) saw Unruh radiation emitted from positrons decelerating in a silicon crystal at CERN.

What is the advantage of this grounding? Everything! First of all, it makes the theory directly testable. QI says that inertia and gravity are due to the push from gradients in Unruh radiation, and you can go and look for that. I’m not saying it’ll be easy, but at least it is possible and conclusive. If there’s no Unruh gradient, then no QI. It also makes specific predictions that no other model does like the galaxy rotation cut-off, that has already been seen. In contrast, if they don’t find the latest version of fuzzy dark matter they just get more money to look for an even more invisible super fuzzy ghost variant...etc.

Also, QI makes physics useful again. By explaining the mechanism of inertia, QI immediately gives us a new handle on nature. Why not make an Unruh gradient ourselves and move things without the need for propellant? The theory also tells you how to do it – Unruh waves are usually ridiculously long (light-years) but to get them to interact with metal structures and form gradients to push with, all you have to do is shorten them by producing very high accelerations, hence the observed thrust from the emdrive which has high acceleration electrons in its cavity walls, or from capacitor drives which highly accelerate electrons. This usefulness will produce a revolution in thrust and energy. Forward-thinking industry already knows this, and QI capacitor drives are just about to be switched on in space by IVO Ltd on a Rogue Space Systems cubesat launched by SpaceX.

Theoretical physics has had the wrong approach since the 1960s and disappeared into comfort, invisibility and untestability, but quantised inertia represents the return of a real physics with consequences (both theoretical and applied). I apologise. Given the state of the world you may not want more excitement right now, but if you can take it, this is of the good kind.

Get access to twice-weekly updates on QI at patreon: https://www.patreon.com/OneSteptoTauCeti

Follow me on X: memcculloch

References

Lynch, M.H., E. Cohen, Y. Hadad, I. Kaminer, 2021. Experimental observations of acceleration-induced thermality. Phys. Rev. D., 104, 025015. https://arxiv.org/abs/1903.00043

The Bullet Cluster Looks Like a QI Effect

The Bullet Cluster is often taken as a proof of dark matter, but dark matter is so flexible that anything could be taken that way. The cluster is shown in the composite picture below (from NASA's Chandra X ray observatory). The pink areas are the visible matter. The bullet, the pink 'cone' to the right, from its symmetry, looks as if it has moved from left to right and has crashed through the pink mass on the left.

Figure 1. The Bullet cluster, visible mass (pink) & inferred dark mass (blue)

By looking at the bending of starlight arriving from behind these masses, astronomers have proposed the presence of their favourite fudge, dark matter, shown by the blue areas. Well, I never did like fudge as a child, and I still don’t, so let’s see if quantised inertia will explain this instead and in a way that does not need fudging.

Quantised inertia predicts that every time the mutual accelerations get very low, and that happens especially along spin axes (see my referenced paper on the flyby anomaly below), then the inertia decreases in a new way and particles, including photons, should bend more under gravity, making it look like there is dark matter when it is actually a QI effect instead. Sure enough, the blue areas are along the spin axis of the cluster (a spin I have deduced quite reasonably from the rotational symmetry of the Bullet, its cone shape.)

Let’s see if the numbers fit. The mass of the Bullet is 2x10^14 Solar masses, and the distance to the centre of the blue area to the right of it, is, roughly 250 kiloparsecs. So the acceleration there is

a = GM/r^2 = 4.7x10^-10 ms^2

By now, if you have been following me for 20 years you may be getting fed up of this number (or values close to it) which crops of everywhere in deep space, but I love to see it. What this means is that the Bullet Cluster, far from proving dark matter, supports QI in two ways. The blue areas are along the axis as predicted by QI, and the acceleration is indeed low enough in the blue areas to make QI effects important.

I hope you have enjoyed this latest Bullet-in, for more like this, but twice a week, please subscribe at my patreon https://www.patreon.com/OneSteptoTauCeti

Reference

McCulloch, M.E., 2008. Modelling the flyby anomalies using a modification of inertia. MNRAS Letters, 389 (1), L57-60 https://academic.oup.com/mnrasl/article/389/1/L57/996711

Request for Support

I've been writing this blog for seventeen years now, and I will continue because I enjoy it and it gets the message out, but I would like to explain my change of circumstances. In 2017, I won $1.3M from DARPA to test whether quantised inertia can indeed produce propulsion and by the end of the project several labs in liaison with me had shown thrust. When the DARPA project started, in 2017, I bought myself out of teaching to work 100% on it. Unfortunately, in 2023 when I went back to the courses I had been teaching, they had shrunk: I was told the students didn't like positioning and matrix algebra anymore. How odd! I guess I had not been there to present it in an accessible manner :) So I was let go. I suspect part of the issue may have been my alternative physics and my non-woke opinions (I went through a disciplinary process for my non-woke comments on twitter in 2021).

Since 2023 I have been applying for jobs in academia, but I'm not getting any responses, which seems strange for a person with a lot of papers, evidence of funding at a high level, and high profile work. I feel a bit like William Shatner after Star Trek TOS ended, slightly famous but in dire straits. As a result, in order to continue I am designing an entirely new career that is anti-fragile, that won't suddenly disappear because my opinion differs from the crowd - freedom is essential for someone who wants to innovate. That's why I'm trying to become a publicly-funded physicist/author. I'm appealing for help from the largely non-woke technically-aware public since group-think seems to have blacklisted me.

The method I'm using so far is Patreon. The deal is that you can pay as little as £3 or 4$ a month to read accessible discussions of new anomalies and developments in quantised inertia. I was always a good teacher at university - I can explain complex things simply (I was told). I write a page or so twice a week and I am putting my papers on there as well, before submission:

https://www.patreon.com/c/OneSteptoTauCeti

There are options to pay £10 or more, which would help. I'm not ashamed to ask that if you do value my work, please do subscribe. My intention is to build an online university that offers a much better version of physics (and indeed the technique of science) than the old universities do: no dark matter, no eleven-dimensional strings, but driven by new observations, more predictive, philosophically coherent, simpler, and with hope for quantum launch, clean energy and interstellar travel (fully backed by evidence). As a student of this university you might be the one to make these things practically possible. It was after all, reading my papers that inspired Frank Becker to suggest capacitors as a solution, and get a patent. It was a talk by me at his astronomy club that caused Steve Cookson to co-publish a paper on wide binaries in a prestigious journal - it's rare for an astronomy club to achieve that. The public can contribute to science, if they keep up with the anomalies and the new wave. My Patreon is a way to do that.

QI is taking off (and I don't just mean the exciting IVO launch of a QI drive in March) and when it does, anyone in the know will be ahead. Besides, anomalies and QI are fascinating in their own right.

"The future belongs to those who show up" - Mark Steyn

Four Books!

So far, I have written four books that cover quantised inertia, among other things like the scientific method and what it is like to be a maverick scientist, from various points of view.

I was invited to write my first book, Physics from the Edge (2014) by World Scientific. The title had three meanings. First of all, quantised inertia's main claim is that the cosmic edge (horizon) affects inertia here, so it is indeed physics from the edge of the cosmos. The second meaning is that I felt myself to be on the edge of the physics community. The third meaning was an allusion to Carrie Fisher's Postcards from the Edge... partly because I always fancied Carrie Fisher. The book introduces QI and some applications of it. You can get a good feel for the early years of QI. The theory was slightly different back then. Many things have improved but some nuances have been lost. It is expensive though, as it was publish as a monograph.

My second book (2021) was called Falling Up. It is a sci-fi novelette, published on Amazon. I wrote it, off and on, from about 2004 to 2021 so it contains bits from the entire history of QI. The antigrav lab scene, for example, was written before I derived QI and was living on a station platform (in a tiny flat I must add!). It has many good reviews on Amazon and 4.7 stars. One reviewer said that "If Frank McCourt was to write a sci-fi novel it would read something like this." Excited by that comment, I read his novel, Angela's Ashes, and it seemed almost grammarless! I'll take it as a compliment anyway.

My third book (2023) was called Hacking the Cosmos, and is also a novelette. It was written more recently, as you will see from the social environment I describe. It introduces QI from the new information standpoint and also describes the feeling of alienation from the physics community that I've felt, almost as if I was indeed guilty of destroying the cosmos. I refer to some of the relevant QI papers in the book.

My fourth book (2024) called Quantised Accelerations is the second QI textbook and was published by Robert Zubrin's Polaris Books. I wanted with this one to demonstrate the old empirical approach (i.e. genuine science) that has been almost entirely lost in these times. The book starts by discussing 54 anomalies that cannot be explained by modern physics. It then introduces QI, and shows how QI explains most of the anomalies. I also discuss applications: thrust, power and interstellar travel, and some consequences for philosophy. I wrote it to be accessible, there are equations, but they are simple, and I drew cartoons and schematics to help explain the ideas. It is still selling well and has 4.7 stars on Amazon.

I have loved writing them, and I hope you enjoy reading them.

A Potted History of QI

2001. Trigger moment. Perhaps this is the point at which it all began. I was working at the Met Office. After the angst of post-docs, a secure ocean modelling research job meant I was able to branch out a little. On 6th February for various reasons I had to hide in the library and there I read about a paper of Haisch, Ruella and Puthoff in New Scientist, wherein they attributed inertia to the zero point field (zpf). I loved the approach. Later I realised it was wrong since they have to hard-wire an arbitrary cutoff to get rid of a background zpf, so in 2006 I developed Quantised Inertia instead which relies on zpf gradients so is not affected by absolute values. This is my method: to not allow anything arbitrary into a theory.

2006. Pioneer. The first paper on Quantised Inertia. I showed that if you assume that inertia is due to Rindler horizons damping Unruh radiation (an excited quantum background / zpf) then this predicted the Pioneer anomaly, the cosmic mass and various other observed oddities.

2012. Galaxies. For a long time I was unable to work out how to apply QI to galaxies, they are more complex than lone spacecraft, but I worked out how to do it in this paper and showed dark matter is emphatically not needed. I did it in more detail in a paper in 2017.

2013. The mechanism. I proposed for the first time a beautiful and direct mechanism for the inertial mass we all know and love. When an object accelerates in one direction, is sees a relativistic horizon in the other direction. This horizon damps the quantum background creating a quantum gradient that pushes back on the object giving it inertia. i.e. inertia is not intrinsic to the object but due to external quantum forces. You might say this is ‘mass without mass’. I also mentioned how to make objects move without propellant: by making artificial horizons (bits of metal).

2014. Textbook1. My first textbook on QI was called Physics from the Edge: full of anecdotes, equations and a few cartoons. It was published by World Scientific, but was not the mass market breakthrough I needed because it was priced as a monograph and too expensive.

2015. I collected data on the apparent thrust of Shawyer’s emdrive and found that QI predicted it very well, especially the effect of adding dielectrics to the cavity. I took this as evidence that my musings on propellant-less thrust in 2013 were not idle.

2017. DARPA said they ‘had been watching me for some time’, and came to visit. I was given $1.3M to test for thrust in the lab. My papers on the emdrive and dielectrics reminded a smart engineer called Frank Becker of some anomalous capacitor tests he once did and he teamed up with Ankur Bhatt to do some tests. In liaison with me they found thrust and then so did other labs including one I set up at Plymouth with a great engineer called Richard Arundal (fun times!).

2019. My Spanish post-doc Jesus Lucio and I published a paper showing that only QI can explain the orbits of wide binary stars. I loved working with Jesus (as I did with Richard).

2020. Unruh Radiation is Real. Michael Lynch and his team made the first observation of Unruh radiation in positrons decelerating in crystals at CERN, and kindly emailed me in some excitement to tell me. This was good news since I’ve been depending on the existence of Unruh radiation for many years – it’s essential to QI.

2023. Space Test. A forward thinking company called IVO Ltd and led by Richard Mansell (a thoroughly decent guy you can’t help but admire) tested a Becker and Bhatt style capacitor in a professional vacuum chamber and saw QI thrust. They then launched a test into space! Unfortunately, the cubesat was lost before the test could be made but they’ll try again in 2025.

2024. Textbook 2. This year I've shown that only QI can explain the orbit of Proxima Centauri, our nearest neighbour in space, which orbits Alpha and Beta Centauri far too fast. I also completed my second textbook, published by the great Robert Zubrin, who is himself a force of nature. I made sure this one was a lot cheaper than the first and it is selling well. In it, I point out 54 anomalies that old physics cannot explain, introduce QI, and show how it predicts these anomalies. I also propose how it could produce new clean energy sources and how it not only explains the orbit of Proxima but how QI thrust could get us there in 10-15 years.

It's been a great adventure, but the best is yet to come...

My New Book: Quantised Accelerations

These are exciting times for Quantised Inertia (QI). I've just published a paper, my first in three years, showing that the only dynamical model that can predict the orbit of our closest neighbour in space, Proxima Centauri, is, surprise, surprise QI! This paper was just accepted and published by the Monthly Notices of the Royal Astronomical Society no less (see references).

Also, my new book on quantised inertia is available from Amazon next month, on the 15th July (see references). I've been working on this book for seven years, and it is, I hope, nothing less than an empirical reboot for theoretical physics. Like Gaul, in Caesar's eyes, the book is divided into three parts:

In the first part I have no mercy on the standard model of physics and I discuss 54 observed anomalies that prove that the old physics just can't cope anymore. These range from the large-scale cosmic acceleration which makes a mockery of any pretence of conservation of energy in physics, down through the well-known galaxy rotation problem that gave rise to the need for the awfully arbitrary dark matter, the wayward asteroid Oumuamua, down through laboratory thrust oddities, the Abraham-Minkowski paradox, the long running controversy of cold fusion and the proton radius anomaly. This is a scale range from 10^-15 to 10^26 metres.

Then, just when you are giving up hope that any physics can explain these diverse anomalies, I introduce quantised inertia and show that it predicts what people have been calling the usual property of inertia, but with a slight change that predicts the anomalies as well. It gets rid of the gravitational constant, which turns out to be the speed of light squared times the cosmic scale divided by its mass. Happily, one less constant to learn at university (I always found it to be a perfectly acceptable constant but with Frankenstein units).

Just as you are breathing a sign of relief that physics might look up from its invisible entities and untestable strings, I introduce all the applications of QI which include much better satellite thrusters, the ability to get to Proxima Centauri (yes, the same) in less than 15 or so years, self-thrusting materials, FTL comms and a possible way to generate energy from it.

My overall goal is to put physics back into its best mode: first look, then think, then get busy!

References

Paper: McCulloch, M.E., 2024. Testing Quantised inertia on Proxima Centauri. MNRAS, 352, 1, L67-69. https://academic.oup.com/mnrasl/article/532/1/L67/7682393

Book: McCulloch, M.E., 2024. Quantised Accelerations: from anomalies to new physics. Polaris Books. https://www.amazon.co.uk/Quantised-Accelerations-Anomalies-New-Physics/dp/B0D53HLDD3

The Hubble "Tension"

If you say boo to a goose and it flies away, rather than attacking you as they used to at York University, then the sounds you hear coming from it will shift to a lower frequency as the waves from your point of view are spread out. This is the Doppler effect and applies to light waves as well. As we know, Edwin Hubble noticed that the light from distant galaxies was red shifted, that is, the wavelength of the light we received from them was longer, implying that the galaxies were moving away from us and that the further ones were moving away faster than the closer ones. This was taken to mean that all the galaxies were moving away from a common centre as if there had been a Big Bang (or a Big Boo) 13.6 billion years in the past.

Looking at local galaxies, the Hubble expansion rate has been measured to be 73 km/s/Mpc. That is, galaxies one megaparsec (Mpc) away from us are apparently moving away from us at 73 km/s.

Recently, a new method was devised to calculate the Hubble constant from observations of the Cosmic Microwave Background, that represents the cosmos long ago at a redshift of Z=1000, and then extrapolating forward using standard models assuming dark matter and dark energy. Perhaps not surprisingly they got a different answer: 67.7 km/s/Mpc.

This discrepancy is now much bigger than the uncertainties in these two numbers, so it is significant (Reiss et al., 2019). As is usual in physics now, to avoid offending anyone, this is called "The Hubble Tension", but in fact it is a falsification of the present model (as stated, the difference is larger than the error bars).

What does QI have to say about this? Well, there is an interesting link up. If you look at the difference in these speeds you get 73 - 67.7 = 5.3 km/s/MPc. Scaling this up to the speed at the edge of the cosmos you get 155,000 km/s and if you calculate an acceleration from this by dividing by the age of the universe you get

Acceleration = 3.8x10^-10 m/s^2

This is the mutual acceleration of both sides of the cosmos and we just want that of one, so when we divide by two we get about 2x10^-10 m/s^2. Those who know about quantised inertia, QI (surely most of you reading by now) will see immediately that this is the minimum cosmic acceleration predicted by QI as 2c^2/CosmicScale = 2x10^-10 m/s^2. So maybe the Hubble "Tension" is just the fact that they left QI out of their model!

Note that there is probably more to this, as I'm not sure I believe in the physical acceleration model either, but you must admit this does all fit rather well!

References

Riess, A. et al., 2019. Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, Volume 876, Issue 1, article id. 85, 13 pp.

The 18th Birthday of Quantised Inertia

Recently, last Thursday, it was the 18^th Birthday of Quantised Inertia. Back then, in 2006 I was a humble ocean and wave modeller at the UK Met Office in Exeter, with a hobby of thinking about physics in the evenings. It was on the 1^st February, 2006 that I first realised that Newton’s First Law was slightly wrong (ie: QI) and that this was a big step

I gave my first talk on QI (then I called it MiHsC) later that year at the Alternative Gravities Conference at the Royal Observatory in Edinburgh where I had the last talk, and I nearly did not get to speak as they all wanted to go to the pub! In 2007 I published the first paper on QI. One of my colleagues at the Met Office told me I shouldn’t have such grandiose dreams, weathermen should stay below Karman Line. I submitted anyway and my first paper on QI was accepted by MNRAS (a prestigious astronomical journal). The reviewer was delightfully amused that I’d used the term ‘forecast’ instead of ‘predict’ and did not quite believe QI, he said, but he also said it was better than the alternatives he'd seen already published, so why not publish?

By 2008, I’d published enough papers to leave the Met Office and get into academia at Plymouth University, lecturing in geomatics (the maths of positioning in space) which was a subject vague enough to fit. I enjoyed the teaching, and my courses on GPS Positioning stimulated me to develop a better way to formulate QI, using uncertainty in position and information. I finally managed to show that QI predicts galaxy rotation without dark matter which is a massive result, and very clear in that even the onset of the anomaly is predicted well, and I was invited by World Scientific to publish a monograph.

In some papers I mentioned producing thrust from QI, and a few years later DARPA got in touch (2016), said they'd been "following my work for some time", and invited me to apply for funds. I applied and won $1.3M to test for what I’d predicted: thrust from highly accelerated objects in cavities. We first tried photon cavities. I used labs in Germany and Spain, which I was soon unable to visit due to covid, but the photons were too light (pun intended) to work. Fortunately along came engineers Becker and Bhatt who'd read my papers and they suggested electron cavities instead (capacitors). That seemed to work in their lab and IVO Ltd (Richard Mansell) confirmed and improved on it. I managed to get DARPA funds to Plymouth to replicate it with engineer Richard Arundal (a paper is in review) and now IVO have launched a test into space via SpaceX and Rogue Space Systems! Another recent development is that Lynch et al. (2021) have finally confirmed Unruh radiation using CERN data. Morgan Lynch emailed me excitedly to tell me. This is good for QI, which has been assuming its existence for 18 years!

Now I am temporarily between jobs, busy with new QI books (one sci-fi and one text book) and papers, but given the crazy acceleration of the past few years, there is some relief in pausing to decide how best to progress. QI (my hobby) is so big now: a radical change to physics, thrust, clean energy, interstellar travel... It needs development for the sake of getting humanity to the next level, yes, but to avoid burn out I do need to get back to the feeling that this is a deep scientific exploration & not just the race of all time.

Keep Calm and Quantise Inertia!

QI Takes Off

It is thrilling to know that the first spacecraft designed to test for thrust from quantised inertia (QI) is now up there. Designed and built by IVO Ltd, and launched on the 11th November aboard a SpaceX, Falcon 9 and sharing a cubesat belonging to Rogue Space Systems, it is now in a good low Earth orbit and IVO are monitoring it for a month to get statistics good enough to provide a baseline. At some point soon they will switch on the quantum drive and see if the orbit changes. If it does then the world will change with it. Very appropriately to the spirit of QI physics which has always been open to all, hence this blog, you can monitor the orbital data of the satellite (called Barry-1) for yourself here:

https://db.satnogs.org/satellite/QDDY-8878-5291-1819-3935#data

For more information you can see an article in The Debrief by Christopher Plain, with quotes from Richard Mansell, the CEO of IVO Ltd:

https://thedebrief.org/exclusive-the-impossible-quantum-drive-that-defies-known-laws-of-physics-was-just-launched-into-space/

There's also a good article in Forbes by David Hambling, who has been following QI and related issues for a few years now, so he has a good grasp of it. It has quotes from Shawyer and myself:

https://www.forbes.com/sites/davidhambling/2023/11/17/controversial-quantum-space-drive-in-orbital-test-others-to-follow/?sh=a2c9538742a7

Little did I know when I started scribbling on bits of paper back in 2006 (I was then a lowly scientist at the Met Office), that two years later I'd get an academic post and start this blog, six years later be invited to write a book, 11 years later get £1M in DARPA funds and 17 years later a US company would launch a test of QI into space! More will follow. It's been a thrilling ride, with a few temporary downs, but massive ups, including this launch. The pace is accelerating as well. My main hope is that I can continue to think calmly about fundamental physics as this all takes off!

Free Fall, & The Lord Hates a Coward

I had a bit of an epiphany recently while explaining the weightlessness of free fall to my son - a way to see it using horizons. The insight that Einstein had in 1907 that a falling man would not feel his own weight was apparently the happiest thought of his life, and although I admire Einstein, I've always been wary about this evidence-less thought. It is almost as if Einstein was trying to convince himself. The insight proved to him that inertial mass (the resistance to acceleration) was equivalent to the gravitational mass (the attraction to other matter) and so they cancelled out. Lovely and symmetrical, but 100% true?

This is called the equivalence principle and it has been tested many times by experiments that are far more accurate versions of Galileo's dropping of two heavy balls from the tower of Pisa (I often had the amusing thought that he was aiming for one of his many critics). The balls hit the ground at the same time, thus proving the equivalence of inertial and gravitational mass. Or does it?

There is a loop hole. The change of inertial mass in quantised inertia is such that the effect is independent of the mass. The acceleration changes to: a = GM/r^2 + 2c^2/Theta. This has a constant second term, which means that both balls would still fall together, but a little faster. This means the experiments done so far (based on the two balls) will be blind to QI. They need to look at speed of fall instead.

The epiphany I had was imagining the spacecraft we were watching on screen (in Independence Day), and getting rid of all fields and only thinking of horizons. As the craft accelerates towards Earth there is a single Rindler horizon above it which damps the Unruh radiation above it pulling it up (inertia), and many little horizons caused by atoms/matter in the Earth below it damping the fields there and pulling it down (gravity). Whereas in general relativity the path of the craft is along an abstract vector in space-time (a thing that can never be tested for directly), in QI the balance is caused by horizons and their damping of the Unruh field, something that can be tested for (Unruh radiation has now been detected, see reference).

Modern theoretical physics disdains the idea of testability, but I do not, and it has been found that the best theories are always the testable ones, almost as if the cosmos gives us a reward for sticking our necks out. "Well, the Lord hates a coward." - Jim Malone.

References

Lynch et al., 2021. Experimental Observation of Acceleration-Induced Thermality. Phys. Rev. D 104, 025015. https://arxiv.org/abs/1903.00043